Advantages of a sling vs a stroller:
- You can go on mall escalators
- You can fit in tight aisles in clothing stores
- You can fit in a regular public bathroom stall, or a change room
- You can go up stairs
- You can go easily over curbs
- You can go easily over rough terrain, sand, gravel, grass, snow and ice
- Your 10-lb baby weighs 10 pounds, instead of the 50lb (or whatever) stroller
- Much easier on the bus
- When driving somewhere, upon arrival you just pop baby into the sling which you're probably already wearing, no need to transport a stroller and set it up.
- Upon departing, no need to take down the stroller and fit it back into your car...
- When going to the movies or Marineland or amusement parks etc, most places require you to park the stroller outside and carry baby into the venue anyway!
- If baby is fussy in the stroller, you have to stop, go around to the front (since most strollers are front-facing), kneel down, figure out the problem, fix the problem, get baby settled, before you can start walking again. With a sling, you can keep walking while chatting with baby about the problem.
- If baby's fussiness is because they want to be out (like with older toddlers who want to walk), then you're left with a toddler on the go AND an empty stroller to push around. With a sling, you just have the toddler.
- Often in strollers, babies are 'buried', either under canopies or blankets or rain guards or whatever. No interaction with the world.
- Sling babies are at "conversation height" and learn more by observing you interacting with other people and the world than they do down at stroller height.
These are only the reasons off the top of my head, and only in specific reference to comparison with strollers. There are of course many other advantages as well, some already mentioned.